Picking out the right undertone of red lipstick doesn't have to be rocket science. For the most part there are no real rules, but there are some suggestions to follow depending on your skin and hair tone. In the end you should always go with what you're comfortable with, and what makes you feel gorgeous.
You Have Fair Skin and Light Hair:
You should focus on yellow or orange based bright red lipstick colors. By choosing the yellow/orange undertone you are complimenting the lighter tones of your hair, since lighter tones cannot handle quite as much coloring as darker tones.
You Have Darker Skin and Darker Hair:
You should focus on blue based reds, even the ones that fall into the pinky tones. Your tones are opposite of the fair skinned and light haired. The darker hair tones and darker skin tones can withstand stronger and bolder colors without looking garish. Plus, the darker your skin tone the more color you will need or it will end up looking nonexistent on your lips or just end up washing out your complexion all together.
So what do you do if you have dark hair and pale skin?
This is my situation and it really depends on the undertones of your skin. Personally, I can get away with some yellow/orange based reds as long as they do not have very prominent undertones. However, because of the pink tones in my skin, I tend to go toward the blue based reds. For most darker-haired people I believe that blue undertone reds are the prettiest shades, plus it's easier to find a "true" red in that family.
What do you do if you have light hair and darker skin?
Personally, I find that most of the time your hair shade will influence the undertone of your lipstick than just your skin tone. If you have had a good summer and you look like a bronze Goddess, then reach for a yellow/orange undertone red lipstick first. Chances are you will find a good shade for you here first since you have a lighter shade of hair and your skin is still glowing from the summer sun. On the other hand, if you have naturally dark skin and you have lightened your hair then don't be afraid to experiment with yellow/orange tones, but remember to go darker so it doesn't disappear when you apply it. Keep in mind that if you have a natural very dark skin tone then you should try a blue-based shade first and then see if you can find a good deep yellow/orange shade.